Manifold array processor

ABSTRACT

An array processor includes processing elements arranged in clusters which are, in turn, combined in a rectangular array. Each cluster is formed of processing elements which preferably communicate with the processing elements of at least two other clusters. Additionally each inter-cluster communication path is mutually exclusive, that is, each path carries either north and west, south and east, north and east, or south and west communications. Due to the mutual exclusivity of the data paths, communications between the processing elements of each cluster may be combined in a single inter-cluster path. That is, communications from a cluster which communicates to the north and east with another cluster may be combined in one path, thus eliminating half the wiring required for the path. Additionally, the length of the longest communication path is not directly determined by the overall dimension of the array, as it is in conventional torus arrays. Rather, the longest communications path is limited only by the inter-cluster spacing. In one implementation, transpose elements of an N×N torus are combined in clusters and communicate with one another through intra-cluster communications paths. Since transpose elements have direct connections to one another, transpose operation latency is eliminated in this approach. Additionally, each PE may have a single transmit port and a single receive port. As a result, the individual PEs are decoupled from the topology of the array.

This is a continuation of allowed application Ser. No. 09/323,609 filedon Jun. 1, 1999 now U.S. Pat. No. 6,338,129, which is in turn a divisionof application Ser. No. 08/885,310 filed on Jun. 30, 1997, now U.S. Pat.No. 6,023,753.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to processing systems in general and, morespecifically, to parallel processing architectures.

2. Description of the Related Art

Many computing tasks can be developed that operate in parallel on data.The efficiency of the parallel processor depends upon the parallelprocessor's architecture, the coded algorithms, and the placement ofdata in the parallel elements. For example, image processing, patternrecognition, and computer graphics are all applications which operate ondata that is naturally arranged in two- or three-dimensional grids. Thedata may represent a wide variety of signals, such as audio, video,SONAR or RADAR signals, by way of example. Because operations such asdiscrete cosine transforms (DCT), inverse discrete cosine transforms(IDCT), convolutions, and the like which are commonly performed on suchdata may be performed upon different grid segments simultaneously,multiprocessor array systems have been developed which, by allowing morethan one processor to work on the task at one time, may significantlyaccelerate such operations. Parallel processing is the subject of alarge number patents including U.S. Pat. Nos. 5,065,339; 5,146,543;5,146,420; 5,148,515; 5,546,336; 5,542,026; 5,612,908 and 5,577,262;European Published Application Nos. 0,726,529 and 0,726,532 which arehereby incorporated by reference.

One conventional approach to parallel processing architectures is thenearest neighbor mesh connected computer, which is discussed in R.Cypher and J. L. C. Sanz, SIMD Architectures and Algorithms for ImageProcessing and Computer Vision, IEEE Transactions on Acoustics, Speechand Signal Processing, Vol. 37, No. 12, pp. 2158-2174, December 1989; K.E. Batcher, Design of a Massively Parallel Processor, IEEE Transactionson Computers, Vol. C-29 No. 9, pp. 836-840 September 1980; and L. Uhr,Multi-Computer Architectures for Artificial Intelligence, New York,N.Y., John Wiley & Sons, Ch. 8, p. 97, 1987.

In the nearest neighbor torus connected computer of FIG. 1A multipleprocessing elements (PEs) are connected to their north, south, east andwest neighbor PEs through torus connection paths MP and all PEs areoperated in a synchronous single instruction multiple data (SIMD)fashion. Since a torus connected computer may be obtained by addingwraparound connections to a mesh-connected computer, a mesh-connectedcomputer, one without wraparound connections, may be thought of as asubset of torus connected computers. As illustrated in FIG. 1B, eachpath MP may include T transmit wires and R receive wires, or asillustrated in FIG. 1C, each path MP may include B bidirectional wires.Although unidirectional and bidirectional communications are bothcontemplated by the invention, the total number of bus wires, excludingcontrol signals, in a path will generally be referred to as k wireshereinafter, where k=B in a bidirectional bus design and k=T+R in aunidirectional bus design. It is assumed that a PE can transmit data toany of its neighboring PEs, but only one at a time. For example, each PEcan transmit data to its east neighbor in one communication cycle. It isalso assumed that a broadcast mechanism is present such that data andinstructions can be dispatched from a controller simultaneously to allPEs in one broadcast dispatch period.

Although bit-serial inter-PE communications are typically employed tominimize wiring complexity, the wiring complexity of a torus-connectedarray nevertheless presents implementation problems. The conventionaltorus-connected array of FIG. 1A includes sixteen processing elementsconnected in a four by four array 10 of PEs. Each processing elementPE_(i,j) is labeled with its row and column number i and j,respectively. Each PE communicates to its nearest North (N), South (S),East (E) and West (W) neighbor with point to point connections. Forexample, the connection between PE_(0,0) and PE_(3,0) shown in FIG. 1Ais a wraparound connection between PE_(0,0)'s N interface and PE_(3,0)'ssouth interface, representing one of the wraparound interfaces thatforms the array into a torus configuration. In such a configuration,each row contains a set of N interconnections and, with N rows, thereare N² horizontal connections. Similarly, with N columns having Nvertical interconnections each, there are N² vertical interconnections.For the example of FIG. 1A, N=4. The total number of wires, such as themetallization lines in an integrated circuit implementation in an N×Ntorus-connected computer including wraparound connections, is therefore2 kN², where k is the number of wires in each interconnection. Thenumber k may be equal to one in a bit serial interconnection. Forexample with k=1 for the 4×4 array 10 as shown in FIG. 1A, 2 kN²=32.

For a number of applications where N is relatively small, it ispreferable that the entire PE array is incorporated in a singleintegrated circuit. The invention does not preclude implementationswhere each PE can be a separate microprocessor chip, for example. Sincethe total number of wires in a torus connected computer can besignificant, the interconnections may consume a great deal of valuableintegrated circuit “real estate”, or the area of the chip taken up.Additionally, the PE interconnection paths quite frequently cross overone another complicating the IC layout process and possibly introducingnoise to the communications lines through crosstalk. Furthermore, thelength of wraparound links, which connect PEs at the North and South andat the East and West extremes of the array, increase with increasingarray size. This increased length increases each communication line'scapacitance, thereby reducing the line's maximum bit rate andintroducing additional noise to the line.

Another disadvantage of the torus array arises in the context oftranspose operations. Since a processing element and its transpose areseparated by one or more intervening processing elements in thecommunications path, latency is introduced in operations which employtransposes. For example, should the PE_(2,1) require data from itstranspose, PE_(1,2), the data must travel through the interveningPE_(1,1) or PE_(2,2). Naturally, this introduces a delay into theoperation, even if PE_(1,1) and PE_(2,2) are not otherwise occupied.However, in the general case where the PEs are implemented asmicroprocessor elements, there is a very good probability that PE_(1,1)and PE_(2,2) will be performing other operations and, in order totransfer data or commands from PE_(1,2) to PE_(2,1), they will have toset aside these operations in an orderly fashion. Therefore, it may takeseveral operations to even begin transferring the data or commands fromPE_(1,2) to PE_(1,1) and the operations PE_(1,1) was forced to set asideto transfer the transpose data will also be delayed. Such delayssnowball with every intervening PE and significant latency is introducedfor the most distant of the transpose pairs. For example thePE_(3,1)/PE_(1,3) transpose pair of FIG. 1A, has a minimum of threeintervening PEs, requiring a latency of four communication steps andcould additionally incur the latency of all the tasks which must be setaside in all those PEs in order to transfer data between PE_(3,1) andPE_(1,3) in the general case.

Recognizing such limitations of torus connected arrays, new approachesto arrays have been disclosed in U.S. Pat. No. 5,612,908; A MassivelyParallel Diagonal Fold Array Processor, G. G. Pechanek et al., 1993International Conference on Application Specific Array Processors, pp.140-143, Oct. 25-27, 1993, Venice, Italy, and Multiple Fold ClusteredProcessor Torus Array, G. G. Pechanek, et. al., Proceedings Fifth NASASymposium on VLSI Design, pp. 8.4.1-11, Nov. 4-5, 1993, University ofNew Mexico, Albuquerque, N.Mex. which are incorporated by referenceherein in their entirety. The operative technique of these torus arrayorganizations is the folding of arrays of PEs using the diagonal PEs ofthe conventional nearest neighbor torus as the foldover edge. Asillustrated in the array 20 of FIG. 2, these techniques may be employedto substantially reduce inter-PE wiring, to reduce the number and lengthof wraparound connections, and to position PEs in close proximity totheir transpose PEs. This processor array architecture is disclosed, byway of example, in U.S. Pat. Nos. 5,577,262, 5,612,908, and EP 0,726,532and EP 0,726,529 which were invented by the same inventor as the presentinvention and is incorporated herein by reference in its entirety. Whilesuch arrays provide substantial benefits over the conventional torusarchitecture, due to the irregularity of PE combinations, for example ina single fold diagonal fold mesh, some PEs are clustered “in twos”,others are single, in a three fold diagonal fold mesh there are clustersof four PEs and eight PEs. Due to an overall triangular shape of thearrays, the diagonal fold type of array presents substantial obstaclesto efficient, inexpensive integrated circuit implementation.Additionally, in a diagonal fold mesh as in EP 0,726,532 and EP0,726,529, and other conventional mesh architectures, theinterconnection topology is inherently part of the PE definition. Thisfixes the PE's position in the topology, consequently limiting thetopology of the PEs and their connectivity to the fixed configurationthat is implemented. Thus, a need exists for further improvements inprocessor array architecture and processor interconnection.

SUMMARY OF THE INVENTION

The present invention is directed to an array of processing elementswhich substantially reduce the array's interconnection wiringrequirements when compared to the wiring requirements of conventionaltorus processing element arrays. In a preferred embodiment, one array inaccordance with the present invention achieves a substantial reductionin the latency of transpose operations. Additionally, the inventivearray decouples the length of wraparound wiring from the array's overalldimensions, thereby reducing the length of the longest interconnectionwires. Also, for array communication patterns that cause no conflictbetween the communicating PEs, only one transmit port and one receiveport are required per PE, independent of the number of neighborhoodconnections a particular topology may require of its PE nodes. Apreferred integrated circuit implementation of the array includes acombination of similar processing element clusters combined to present arectangular or square outline. The similarity of processing elements,the similarity of processing element clusters, and the regularity of thearray's overall outline make the array particularly suitable forcost-effective integrated circuit manufacturing.

To form an array in accordance with the present invention, processingelements may first be combined into clusters which capitalize on thecommunications requirements of single instruction multiple data (“SIMD”)operations. Processing elements may then be grouped so that the elementsof one cluster communicate within a cluster and with members of only twoother clusters. Furthermore, each cluster's constituent processingelements communicate in only two mutually exclusive directions with theprocessing elements of each of the other clusters. By definition, in aSIMD torus with unidirectional communication capability, the North/Southdirections are mutually exclusive with the East/West directions.Processing element clusters are, as the name implies, groups ofprocessors formed preferably in close physical proximity to one another.In an integrated circuit implementation, for example, the processingelements of a cluster preferably would be laid out as close to oneanother as possible, and preferably closer to one another than to anyother processing element in the array. For example, an arraycorresponding to a conventional four by four torus array of processingelements may include four clusters of four elements each, with eachcluster communicating only to the North and East with one other clusterand to the South and West with another cluster, or to the South and Eastwith one other cluster and to the North and West with another cluster.By clustering PEs in this manner, communications paths between PEclusters may be shared, through multiplexing, thus substantiallyreducing the interconnection wiring required for the array.

In a preferred embodiment, the PEs comprising a cluster are chosen sothat processing elements and their transposes are located in the samecluster and communicate with one another through intra-clustercommunications paths, thereby eliminating the latency associated withtranspose operations carried out on conventional torus arrays.Additionally, since the conventional wraparound path is treated the sameas any PE-to-PE path, the longest communications path may be as short asthe inter-cluster spacing, regardless of the array's overall dimension.According to the invention an N×M torus may be transformed into an arrayof M clusters of N PEs, or into N clusters of M PEs.

These and other features, aspects and advantages of the invention willbe apparent to those skilled in the art from the following detaileddescription, taken together with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a block diagram of a conventional prior art 4×4 nearestneighbor connected torus processing element (PE) array;

FIG. 1B illustrates how the prior art torus connection paths of FIG. 1Amay include T transmit and R receive wires;

FIG. 1C illustrates how prior art torus connection paths of FIG. 1A mayinclude B bidirectional wires;

FIG. 2 is a block diagram of a prior art diagonal folded mesh;

FIG. 3A is a block diagram of a processing element which may suitably beemployed within the PE array of the present invention;

FIG. 3B is a block diagram of an alternative processing element whichmay suitably be employed within the PE array of the present invention;

FIG. 4 is a tiling of a 4×4 torus which illustrates all the torus'sinter-PE communications links;

FIGS. 5A through 5G are tilings of a 4×4 torus which illustrate theselection of PEs for cluster groupings in accordance with the presentinvention;

FIG. 6 is a tiling of a 4×4 torus which illustrates alternative groupingof PEs for clusters;

FIG. 7 is a tiling of a 3×3 torus which illustrates the selection of PEsfor PE clusters;

FIG. 8 is a tiling of a 3×5 torus which illustrates the selection of PEsfor PE clusters;

FIG. 9 is a block diagram illustrating an alternative, rhombus/cylinderapproach to selecting PEs for PE clusters;

FIG. 10 is a block diagram which illustrates the inter-clustercommunications paths of the new PE clusters;

FIGS. 11A and 11B illustrate alternative rhombus/cylinder approaches toPE cluster selection;

FIG. 12 is a block diagram illustration of the rhombus/cylinder PEselection process for a 5×4 PE array;

FIG. 13 is a block diagram illustration of the rhombus/cylinder PEselection process for a 4×5 PE array;

FIG. 14 is a block diagram illustration of the rhombus/cylinder PEselection process for a 5×5 PE array;

FIGS. 15A through 15D are block diagram illustrations of inter-clustercommunications paths for 3, 4, 5, and 6 cluster by 6 PE arrays,respectively;

FIG. 16 is a block diagram illustrating East/South communications pathswithin an array of four four-member clusters;

FIG. 17 is a block diagram illustration of East/South and West/Northcommunications paths within an array of four four-member clusters;

FIG. 18 is a block diagram illustrating one of the clusters of theembodiment of FIG. 17, which illustrates in greater detail a clusterswitch and its interface to the illustrated cluster;

FIGS. 19A and 19B illustrate a convolution window and convolution path,respectively, employed in an exemplary convolution which mayadvantageously be carried out on the new array processor of the presentinvention;

FIGS. 19C and 19D are block diagrams which respectively illustrate aportion of an image within a 4×4 block and the block loaded intoconventional torus locations; and

FIGS. 20A through 24B are block diagrams which illustrate the state of amanifold array in accordance with the present invention at the end ofeach convolution operational step.

DETAILED DESCRIPTION

In one embodiment, a new array processor in accordance with the presentinvention combines PEs in clusters, or groups, such that the elements ofone cluster communicate with members of only two other clusters and eachcluster's constituent processing elements communicate in only twomutually exclusive directions with the processing elements of each ofthe other clusters. By clustering PEs in this manner, communicationspaths between PE clusters may be shared, thus substantially reducing theinterconnection wiring required for the array. Additionally, each PE mayhave a single transmit port and a single receive port or, in the case ofa bidirectional sequential or time sliced transmit/receive communicationimplementation, a single transmit/receive port. As a result, theindividual PEs are decoupled from the topology of the array. That is,unlike a conventional torus connected array where each PE has fourbidirectional communication ports, one for communication in eachdirection, PEs employed by the new array architecture need only have oneport. In implementations which utilize a single transmit and a singlereceive port, all PEs in the array may simultaneously transmit andreceive. In the conventional torus, this would require four transmit andfour receive ports, a total of eight ports, per PE, while in the presentinvention, one transmit port and one receive port, a total of two ports,per PE are required.

In one presently preferred embodiment, the PEs comprising a cluster arechosen so that processing elements and their transposes are located inthe same cluster and communicate with one another through intra-clustercommunications paths. For convenience of description, processingelements are referred to as they would appear in a conventional torusarray, for example, processing element PE_(0,0) is the processingelement that would appear in the “Northwest” corner of a conventionaltorus array. Consequently, although the layout of the new cluster arrayis substantially different from that of a conventional array processor,the same data would be supplied to corresponding processing elements ofthe conventional torus and new cluster arrays. For example, the PE_(0,0)element of the new cluster array would receive the same data to operateon as the PE_(0,0) element of a conventional torus-connected array.Additionally, the directions referred to in this description will be inreference to the directions of a torus-connected array. For example,when communications between processing elements are said to take placefrom North to South, those directions refer to the direction ofcommunication within a conventional torus-connected array.

The PEs may be single microprocessor chips that may be of a simplestructure tailored for a specific application. Though not limited to thefollowing description, a basic PE will be described to demonstrate theconcepts involved. The basic structure of a PE 30 illustrating onesuitable embodiment which may be utilized for each PE of the new PEarray of the present invention is illustrated in FIG. 3A. For simplicityof illustration, interface logic and buffers are not shown. A broadcastinstruction bus 31 is connected to receive dispatched instructions froma SIMD controller 29, and a data bus 32 is connected to receive datafrom memory 33 or another data source external to the PE 30. A registerfile storage medium 34 provides source operand data to execution units36. An instruction decoder/controller 38 is connected to receiveinstructions through the broadcast instruction bus 31 and to providecontrol signals 21 to registers within the register file 34 which, inturn, provide their contents as operands via path 22 to the executionunits 36. The execution units 36 receive control signals 23 from theinstruction decoder/controller 38 and provide results via path 24 to theregister file 34. The instruction decoder/controller 38 also providescluster switch enable signals on an output the line 39 labeled SwitchEnable. The function of cluster switches will be discussed in greaterdetail below in conjunction with the discussion of FIG. 18. Inter-PEcommunications of data or commands are received at receive input 37labeled Receive and are transmitted from a transmit output 35 labeledSend.

FIG. 3B shows an alternative PE representation 30′ that includes aninterface control unit 50 which provides data formatting operationsbased upon control signals 25 received from the instructiondecoder/controller 38. Data formatting operations can include, forexample, parallel to serial and serial to parallel conversions, dataencryption, and data format conversions to meet various standards orinterface requirements.

A conventional 4×4 nearest neighbor torus of PEs of the same type as thePE 30 illustrated in FIG. 3A is shown surrounded by tilings of itself inFIG. 4. The center 4×4 torus 40 is encased by a ring 42 which includesthe wraparound connections of the torus. The tiling of FIG. 4 is adescriptive aid used to “flatten out” the wraparound connections and tothereby aid in explanation of the preferred cluster forming processutilized in the array of one embodiment of the present invention. Forexample, the wraparound connection to the west from PE₀₀, is PE_(0,3)that from the PE_(1,3) to the east is PE_(1,0) etc., as illustratedwithin the block 42. The utility of this view will be more apparent inrelation to the discussion below of FIGS. 5A-5G.

In FIG. 5A, the basic 4×4 PE torus is once again surrounded by tilingsof itself. The present invention recognizes that communications to theEast and South from PE_(0,0) involve PE_(0,1) and PE_(1,0),respectively. Furthermore, the PE which communicates to the east toPE_(1,0) is PE_(1,3) and PE_(1,3) communicates to the South to PE_(2,3).Therefore, combining the four PEs, PE_(0,0), PE_(1,3), PE_(2,2), andPE_(3,1) in one cluster yields a cluster 44 from which PEs communicateonly to the South and East with another cluster 46 which includes PEs,PE_(0,1), PE_(1,0) PE_(2,3) and PE_(3,2). Similarly, the PEs of cluster46 communicate to the South and East with the PEs of cluster 48 whichincludes PEs, PE_(0,2), PE_(1,1) PE_(2,0), and PE_(3,3). The PEs,PE_(0,3), PE_(1,2), PE_(2,1), and PE_(3,0) of cluster 50 communicate tothe South and East with cluster 44. This combination yields clusters ofPEs which communicate with PEs in only two other clusters and whichcommunicate in mutually exclusive directions to those clusters. That is,for example, the PEs of cluster 48 communicate only to the South andEast with the PEs of cluster 50 and only to the North and West with thePEs of cluster 46. It is this exemplary of grouping of PEs which permitsthe inter-PE connections within an array in accordance with the presentinvention to be substantially reduced in comparison with therequirements of the conventional nearest neighbor torus array.

Many other combinations are possible. For example, starting again withPE_(0,0) and grouping PEs in relation to communications to the North andEast yields clusters 52, 54, 56 and 58 of FIG. 5B. These clusters may becombined in a way which greatly reduces the interconnection requirementsof the PE array and which reduces the length of the longest inter-PEconnection. However, these clusters do not combine PEs and theirtransposes as the clusters 44-50 in FIG. 5A do. That is, althoughtranspose pairs PE_(0,2)/PE_(2,0) and PE_(1,3)/PE_(3,1) are contained incluster 56, the transpose pair PE_(0,1)/PE_(1,0) is split betweenclusters 54 and 58. An array in accordance with the presently preferredembodiment employs only clusters such as 44-50 which combine all PEswith their transposes within clusters. For example, in FIG. 5A thePE_(3,1)/PE_(1,3) transpose pair is contained within cluster 44, thePE_(3,2), PE_(2,3) and PE_(1,0)/PE_(0,1) transpose pairs are containedwithin cluster 46, the PE_(0,2)/PE_(2,0) transpose pair is containedwithin cluster 48, and the PE_(3,0)/PE_(0,3) and PE_(2,1)/PE_(1,2)transpose pairs are contained within cluster 50. Clusters 60, 62, 64 and68 of FIG. 5C are formed, starting at PE_(0,0), by combining PEs whichcommunicate to the North and West. Note that cluster 60 is equivalent tocluster 44, cluster 62 is equivalent to cluster 46, cluster 64 isequivalent to cluster 48 and cluster 68 is equivalent to cluster 50.Similarly, clusters 70 through 76 of FIG. 5D, formed by combining PEswhich communicate to the South and West, are equivalent to clusters 52through 58, respectively of FIG. 5B. As demonstrated in FIG. 5E,clusters 45, 47, 49 and 51, which are equivalent to the preferredclusters 48, 50, 44 and 46 may be obtained from any “starting point”within the torus 40 by combining PEs which communicate to the South andEast.

Another clustering is depicted in FIG. 5F where clusters 61, 63, 65, and67 form a criss cross pattern in the tilings of the torus 40. Thisclustering demonstrates that there are a number of ways in which togroup PEs to yield clusters which communicate with two other clusters inmutually exclusive directions. That is, PE_(0,0) and PE_(2,2) of cluster65 communicate to the East with PE_(0,1) and PE_(2,3), respectively, ofcluster 61. Additionally, PE_(1,1) and PE_(3,3) of cluster 65communicate to the West with PE_(1,0) and PE_(3,2), respectively, ofcluster 61. As will be described in greater detail below, the Easterlycommunications paths just described, that is, those between PE_(0,0) andPE_(0,1) and between PE_(2,2) and PE_(2,3), and other inter-clusterpaths may be combined with mutually exclusive inter-clustercommunications paths, through multiplexing for example, to reduce byhalf the number of interconnection wires required for inter-PEcommunications. The clustering of FIG. 5F also groups transpose elementswithin clusters.

One aspect of the new array's scalability is demonstrated by FIG. 5G,where a 4×8 torus array is depicted as two 4×4 arrays 40A and 40B. Onecould use the techniques described to this point to produce eightfour-PE clusters from a 4×8 torus array. In addition, by dividing the4×8 torus into two 4×4 toruses and combining respective clusters intoclusters, that is clusters 44A and 44B, 46A and 46B, and so on, forexample, four eight-PE clusters with all the connectivity and transposerelationships of the 4×4 subclusters contained in the eight four-PEcluster configuration is obtained. This cluster combining approach isgeneral and other scalings are possible.

The presently preferred, but not sole, clustering process may also bedescribed as follows. Given an N×N basic torus PE_(i,j), where i=0, 1,2, . . . N−1 and j=0, 1, 2, . . . N−1, the preferred, South- andEast-communicating clusters may be formed by grouping PE_(i,j),PE_((i+1)(ModN), (j+N−1)(ModN)), PE_((i+2)(ModN), (j+N−2)(ModN)), . . ., PE_((i+N−1)(ModN), (j+N−(N−1))(ModN)). This formula can be rewrittenfor an N×N torus array with N clusters of N PEs in which the clustergroupings can be formed by selecting an i and a j, and then using theformula: PE_((i+a)(ModN), (+N−a)(ModN)) for any i,j and for all a ε{0,1, . . . , N−1}.

FIG. 6 illustrates the production of clusters 44 through 50 beginningwith PE_(1,3) and combining PEs which communicate to the South and East.In fact, the clusters 44 through 50, which are the clusters of thepreferred embodiment of a 4×4 torus equivalent of the new array, areobtained by combining South and East communicating PEs, regardless ofwhat PE within the basic N×N torus 40 is used as a starting point. FIGS.7 and 8 illustrate additional examples of the approach, using 3×3 and3×5 toruses, respectively.

Another, equivalent way of viewing the cluster-building process isillustrated in FIG. 9. In this and similar figures that follow,wraparound wires are omitted from the figure for the sake of clarity. Aconventional 4×4 torus is first twisted into a rhombus, as illustratedby the leftward shift of each row. This shift serves to group transposePEs in “vertical slices” of the rhombus. To produce equal-size clustersthe rhombus is, basically, formed into a cylinder. That is, theleft-most, or western-most, vertical slice 80 is wrapped around to abutthe eastern-most PE_(0,3) in its row. The vertical slice 82 to the eastof slice 80 is wrapped around to abut PE_(0,0) and PE_(1,3), and thenext eastward vertical slice 84 is wrapped around to abut PE_(0,1),PE_(1,0) and PE_(2,3). Although, for the sake of clarity, allconnections are not shown, all connections remain the same as in theoriginal 4×4 torus. The resulting vertical slices produce the clustersof the preferred embodiment 44 through 50 shown in FIG. 5A, the sameclusters produced in the manner illustrated in the discussion related toFIGS. 5A and 6. In FIG. 10, the clusters created in the rhombus/cylinderprocess of FIG. 9 are “peeled open” for illustrative purposes to revealthe inter-cluster connections. For example, all inter-PE connectionsfrom cluster 44 to cluster 46 are to the South and East, as are thosefrom cluster 46 to cluster 48 and from cluster 48 to cluster 50 and fromcluster 50 to cluster 44. This commonality of inter-clustercommunications, in combination with the nature of inter-PEcommunications in a SIMD process permits a significant reduction in thenumber of inter-PE connections. As discussed in greater detail inrelation to FIGS. 16 and 17 below, mutually exclusive communications,e.g., communications to the South and East from cluster 44 to cluster 46may be multiplexed onto a common set of interconnection wires runningbetween the clusters. Consequently, the inter-PE connection wiring ofthe new array, hereinafter referred to as the “manifold array”, may besubstantially reduced, to one half the number of interconnection wiresassociated with a conventional nearest neighbor torus array.

The cluster formation process used to produce a manifold array issymmetrical and the clusters formed by taking horizontal slices of avertically shifted torus are the same as clusters formed by takingvertical slices of a horizontally shifted torus. FIGS. 11A and 11Billustrate the fact that the rhombus/cylinder technique may also beemployed to produce the preferred clusters from horizontal slices of avertically shifted torus. In FIG. 11A the columns of a conventional 4×4torus array are shifted vertically to produce a rhombus and in FIG. 11Bthe rhombus is wrapped into a cylinder. Horizontal slices of theresulting cylinder provide the preferred clusters 44 through 50. Any ofthe techniques illustrated to this point may be employed to createclusters for manifold arrays which provide inter-PE connectivityequivalent to that of a conventional torus array, with substantiallyreduced inter-PE wiring requirements.

As noted in the summary, the above clustering process is general and maybe employed to produce manifold arrays of M clusters containing N PEseach from an N×M torus array. For example, the rhombus/cylinder approachto creating four clusters of five PEs, for a 5×4 torus array equivalentis illustrated in FIG. 12. Note that the vertical slices which form thenew PE clusters, for example, PE_(4,0), PE_(3,1), PE_(2,2), PE_(1,3),and PE_(0,0) maintain the transpose clustering relationship of thepreviously illustrated 4×4 array. Similarly, as illustrated in thediagram of FIG. 13, a 4×5 torus will yield five clusters of four PEseach with the transpose relationship only slightly modified from thatobtained with a 4×4 torus. In fact, transpose PEs are still clusteredtogether, only in a slightly different arrangement than with the 4×4clustered array. For example, transpose pairs PE_(1,0)/PE_(0,1) andPE_(2,3)/PE_(3,2) were grouped in the same cluster within the preferred4×4 manifold array, but they appear, still paired, but in separateclusters in the 4×5 manifold array of FIG. 13. As illustrated in thecluster-selection diagram of FIG. 14, the diagonal PEs, PE_(i,j) wherei=j, in an odd number by odd number array are distributed one per,cluster.

The block diagrams of FIGS. 15A-15D illustrate the inter-clusterconnections of the new manifold array. To simplify the description, inthe following discussion, unidirectional connection paths are assumedunless otherwise stated. Although, for the sake of clarity, theinvention is described with parallel interconnection paths, or buses,represented by individual lines. Bit-serial communications, in otherwords buses having a single line, are also contemplated by theinvention. Where bus multiplexers or bus switches are used, themultiplexer and/or switches are replicated for the number of lines inthe bus. Additionally, with appropriate network connections andmicroprocessor chip implementations of PEs, the new array may beemployed with systems which allow dynamic switching between MIMD, SIMDand SISD modes, as described in U.S. Pat. No. 5,475,856 to P. M. Kogge,entitled, Dynamic Multi-Mode Parallel Processor Array Architecture,which is hereby incorporated by reference.

In FIG. 15A, clusters 80, 82 and 84 are three PE clusters connectedthrough cluster switches 86 and inter-cluster links 88 to one another.To understand how the manifold array PEs connect to one another tocreate a particular topology, the connection view from a PE must bechanged from that of a single PE to that of the PE as a member of acluster of PEs. For a manifold array operating in a SIMD unidirectionalcommunication environment, any PE requires only one transmit port andone receive port, independent of the number of connections between thePE and any of its directly attached neighborhood of PEs in theconventional torus. In general, for array communication patterns thatcause no conflicts between communicating PEs, only one transmit and onereceive port are required per PE, independent of the number ofneighborhood connections a particular topology may require of its PEs.

Four clusters, 44 through 50, of four PEs each are combined in the arrayof FIG. 15B. Cluster switches 86 and communication paths 88 connect theclusters in a manner explained in greater detail in the discussion ofFIGS. 16, 17, and 18 below. Similarly, five clusters, 90 through 98, offive PEs each are combined in the array of FIG. 15C. In practice, theclusters 90-98 are placed as appropriate to ease integrated circuitlayout and to reduce the length of the longest inter-cluster connection.FIG. 15D illustrates a manifold array of six clusters, 99, 100, 101,102, 104, and 106, having six PEs each. Since communication paths 86 inthe new manifold array are between clusters, the wraparound connectionproblem of the conventional torus array is eliminated. That is, nomatter how large the array becomes, no interconnection path need belonger than the basic inter-cluster spacing illustrated by theconnection paths 88. This is in contrast to wraparound connections ofconventional torus arrays which must span the entire array.

The block diagram of FIG. 16 illustrates in greater detail a preferredembodiment of a four cluster, sixteen PE, manifold array. The clusters44 through 50 are arranged, much as they would be in an integratedcircuit layout, in a rectangle or square. The connection paths 88 andcluster switches are illustrated in greater detail in this figure.Connections to the South and East are multiplexed through the clusterswitches 86 in order to reduce the number of connection lines betweenPEs. For example, the South connection between PE_(1,2) and PE_(2,2) iscarried over a connection path 110, as is the East connection fromPE_(2,1) to PE_(2,2). As noted above, each connection path, such as theconnection path 110 may be a bit-serial path and, consequently, may beeffected in an integrated circuit implementation by a singlemetallization line. Additionally, the connection paths are only enabledwhen the respective control line is asserted. These control lines can begenerated by the instruction decoder/controller 38 of each PE_(3,0),illustrated in FIG. 3A. Alternatively, these control lines can begenerated by an independent instruction decoder/controller that isincluded in each cluster switch. Since there are multiple PEs perswitch, the multiple enable signals generated by each PE are compared tomake sure they have the same value in order to ensure that no error hasoccurred and that all PEs are operating synchronously. That is, there isa control line associated with each noted direction path, N for North, Sfor South, E for East, and W for West. The signals on these lines enablethe multiplexer to pass data on the associated data path through themultiplexer to the connected PE. When the control signals are notasserted the associated data paths are not enabled and data is nottransferred along those paths through the multiplexer.

The block diagram of FIG. 17 illustrates in greater detail theinterconnection paths 88 and switch clusters 86 which link the fourclusters 44 through 50. In this figure, the West and North connectionsare added to the East and South connections illustrated in FIG. 16.Although, in this view, each processing element appears to have twoinput and two output ports, in the preferred embodiment another layer ofmultiplexing within the cluster switches brings the number ofcommunications ports for each PE down to one for input and one foroutput. In a standard torus with four neighborhood transmit connectionsper PE and with unidirectional communications, that is, only onetransmit direction enabled per PE, there are four multiplexer or gatedcircuit transmit paths required in each PE. A gated circuit may suitablyinclude multiplexers, AND gates, tristate driver/receivers with enableand disable control signals, and other such interface enabling/disablingcircuitry. This is due to the interconnection topology defined as partof the PE. The net result is that there are 4N² multiple transmit pathsin the standard torus. In the manifold array, with equivalentconnectivity and unlimited communications, only 2N² multiplexed or gatedcircuit transmit paths are required. This reduction of 2N² transmitpaths translates into a significant savings in integrated circuit realestate area, as the area consumed by the multiplexers and 2N² transmitpaths is significantly less than that consumed by 4N² transmit paths.

A complete cluster switch 86 is illustrated in greater detail in theblock diagram of FIG. 18. The North, South, East, and West outputs areas previously illustrated. Another layer of multiplexing 112 has beenadded to the cluster switch 86. This layer of multiplexing selectsbetween East/South reception, labeled A, and North/West reception,labeled B, thereby reducing the communications port requirements of eachPE to one receive port and one send port. Additionally, multiplexedconnections between transpose PEs, PE_(1,3) and PE_(3,1), are effectedthrough the intra-cluster transpose connections labeled T. When the Tmultiplexer enable signal for a particular multiplexer is asserted,communications from a transpose PE are received at the PE associatedwith the multiplexer. In the preferred embodiment, all clusters includetranspose paths such as this between a PE and its transpose PE. Thesefigures illustrate the overall connection scheme and are not intended toillustrate how a multi-layer integrated circuit implementation mayaccomplish the entirety of the routine array interconnections that wouldtypically be made as a routine matter of design choice. As with anyintegrated circuit layout, the IC designer would analyze varioustradeoffs in the process of laying out an actual IC implementation of anarray in accordance with the present invention. For example, the clusterswitch may be distributed within the PE cluster to reduce the wiringlengths of the numerous interfaces.

To demonstrate the equivalence to a torus array's communicationcapabilities and the ability to execute an image processing algorithm onthe Manifold Array, a simple 2D convolution using a 3×3 window, FIG.19A, will be described below. The Lee and Aggarwal algorithm forconvolution on a torus machine will be used. See, S. Y. Lee and J. K.Aggarwal, Parallel 2D Convolution on a Mesh Connected Array Processor,IEEE Transactions on Patter Analysis and Machine Intelligence, Vol.PAMI-9, No. 4, pp. 590-594, July 1987. The internal structure of a basicPE 30, FIG. 3A, is used to demonstrate the convolution as executed on a4×4 Manifold Array with 16 of these PEs. For purposes of this example,the Instruction Decoder/Controller also provides the Cluster Switchmultiplexer Enable signals. Since there are multiple PEs per switch, themultiple enable signals are compared to be equal to ensure no error hasoccurred and all PEs are operating in synchronism.

Based upon the S. Y. Lee and J. K. Aggarwal algorithm for convolution,the Manifold array would desirably be the size of the image, forexample, an N×N array for a N×N image. Due to implementation issues itmust be assumed that the array is smaller than N×N for large N. Assumingthe array size is C×C, the image processing can be partitioned intomultiple C×C blocks, taking into account the image block overlaprequired by the convolution window size. Various techniques can be usedto handle the edge effects of the N×N image. For example, pixelreplication can be used that effectively generates an (N+1)×(N+1) array.It is noted that due to the simplicity of the processing required, avery small PE could be defined in an application specificimplementation. Consequently, a large number of PEs could be placed in aManifold Array organization on a chip thereby improving the efficiencyof the convolution calculations for large image sizes.

The convolution algorithm provides a simple means to demonstrate thefunctional equivalence of the Manifold Array organization to a torusarray for North/East/South/West nearest neighbor communicationoperations. Consequently, the example focuses on the communicationsaspects of the algorithm and, for simplicity of discussion, a very small4×4 image size is used on a 4×4 Manifold array. Larger N×N images can behandled in this approach by loading a new 4×4 image segment into thearray after each previous 4×4 block is finished. For the 4×4 array nowrap around is used and for the edge PEs 0's are received from thevirtual PEs not present in the physical implementation. The processingfor one 4×4 block of pixels will be covered in this operating example.

To begin the convolution example, it is assumed that the PEs havealready been initialized by a SIMD controller, such as controller 29 ofFIG. 3A, and the initial 4×4 block of pixels has been loaded through thedata bus to register R1 in each PE, in other words, one pixel per PE hasbeen loaded. FIG. 19C shows a portion of an image with a 4×4 block to beloaded into the array. FIG. 19D shows this block loaded in the 4×4 toruslogical positions. In addition, it is assumed that the accumulating sumregister R0 in each PE has been initialized to zero. Thoughinconsequential to this algorithm, R2 has also been shown as initializedto zero. The convolution window elements are broadcast one at a time ineach step of the algorithm. These window elements are received intoregister R2. The initial state of the machine prior to broadcasting thewindow elements is shown in FIG. 20A. The steps to calculate the sum ofthe weighted pixel values in a 3×3 neighborhood for all PEs follows.

The algorithm begins with the transmission (broadcasting) of the firstwindow element W00 to all PEs. Once this is received in each PE, the PEscalculate the first R0=R0+R2*R1 or R0=R0+W*P. The result of thecalculation is then communicated to a nearest neighbor PE according tothe convolution path chosen, FIG. 19B. For simplicity of discussion itis assumed that each operational step to be described can be partitionedinto three substeps each controlled by instructions dispatched from thecontroller: a broadcast window element step, a computation step, and acommunications step. It is noted that improvements to this simplifiedapproach can be developed, such as, beginning with major step 2,overlapping the window element broadcast step with the communications ofresult step. These points are not essential to the purpose of thisdescription and would be recognized by one of ordinary skill in the art.A superscript is used to represent the summation step value as theoperation proceeds. As an aid for following the communications of thecalculated values, a subscript on a label indicates the source PE thatthe value was generated in. The convolution path for pixel {i,j} isshown in FIG. 19B. FIGS. 20-24 indicate the state of the Manifold Arrayafter each computation step.

In FIG. 20B, W00 is broadcast to the PEs and each PE calculates R0¹=0+W00*R1 and communicates R0 ¹ to the South PE where the received R0 ¹value is stored in the PEs' register R0.

In FIG. 21A, W10 is broadcast to the PEs and each PE calculates R0 ²=R0¹+W10*R¹ and communicates R0 ² to the South PE where the received R0 ²value is stored in the PEs' register R0.

In FIG. 21B, W20 is broadcast to the PEs and each PE calculates R0 ³=R0²+W20*R¹ and communicates R0 ³ to the East PE where the received R0 ³value is stored in the PEs' register R0.

In FIG. 22A, W21 is broadcast to the PEs and each PE calculates R0 ⁴=R0³+W21*R¹ and communicates R0 ⁴ to the East PE where the received R0 ⁴value is stored in the PEs' register R0.

In FIG. 22B, W22 is broadcast to the PEs and each PE calculates R0 ⁵=R0⁴+W22*R¹ and communicates R0 ⁵ to the North PE where the received R0 ⁵value is stored in the PEs' register R0.

In FIG. 23A, W12 is broadcast to the PEs and each PE calculates R0 ⁶=R0⁵+W12*R¹ and communicates R0 ⁶ to the North PE where the received R0 ⁶value is stored in the PEs' register R0.

In FIG. 23B, W02 is broadcast to the PEs and each PE calculates R0 ⁷=R0⁶+W02*R¹ and communicates R0 ⁷ to the West PE where the received R0 ⁷value is stored in the PEs' register R0.

In FIG. 24A, W01 is broadcast to the PEs and each PE calculates R0 ⁸=R0⁷+W01*R¹ and communicates R0 ⁸ to the South PE where the received R0 ⁸value is stored in the PEs' register R0.

In FIG. 24B, W11 is broadcast to the PEs and each PE calculates R0 ⁹=R0⁸+W11*R¹ and End.

At the end of the above nine steps each PE_(i,j) contains (withreference to FIG. 19B):C _(i,j) =W 00 P _(i−1,j−1) +W 10 P _(i,j−1) +W 20 P _(i+1,j−1) +W 21 P_(i+1,j) +W 22 P _(i+1,j+1) +W 12 P _(i,j+1) +W 02 P _(i−1,j+1) +W 01 P_(i−1,j) +W 11 P _(i,j).

For example, for i=5, and j=6 C_(5,6)=W00P4,5+W10P5,5+W20P6,5+W21P6,6+W22P6,7+W12P5,7+W02P4,7+W01P4,6+W11P5,6.

It is noted that at the completion of this example, given the operatingassumptions, four valid convolution values have been calculated, namelythe ones in PEs {(1,1), (1,2), (2,1), (2,2)}. This is due to the edgeeffects as discussed previously. Due to the simple nature of the PEneeded for this algorithm, a large number of PEs can be incorporated ona chip, thereby greatly increasing the efficiency of the convolutioncalculation for large image sizes.

The above example demonstrates that the Manifold Array is equivalent inits communications capabilities for the four North, East, South, andWest—communications directions of a standard torus while requiring onlyhalf the wiring expense of the standard torus. Given the ManifoldArray's capability to communicate between transpose PEs, implementedwith a regular connection pattern, minimum wire length, and minimumcost, the Manifold Array provides additional capabilities beyond thestandard torus. Since the Manifold Array organization is more regular asit is made up of the same size clusters of PEs while still providing thecommunications capabilities of transpose and neighborhoodcommunications, it represents a superior design to the standard anddiagonal fold toruses of the prior art.

The foregoing description of specific embodiments of the invention hasbeen presented for the purposes of illustration and description. It isnot intended to be exhaustive or to limit the invention to the preciseforms disclosed, and many modifications and variations are possible inlight of the above teachings. The embodiments were chosen and describedin order to best explain the principles of the invention and itspractical application, to thereby enable others skilled in the art tobest utilize the invention. It is intended that the scope of theinvention be limited only by the claims appended hereto.

1. An interconnection system for a plurality of processing elements(PEs), each PE having a communications port for transmitting andreceiving data and commands, each PE corresponding to a position of amatrix element where the position of the matrix element has at least aNorth, East, South, or West matrix position neighbor, a pair of matrixneighbors is mutually exclusive when one neighbor is either in the Northor South direction relative to the position of the matrix element andthe other neighbor is either in the East or West direction relative tothe position, the interconnection system comprising: a plurality ofclusters of PEs, each cluster comprising a portion of the plurality ofPEs; and a cluster switch connected to said PEs in each cluster, saidportion of the plurality of PEs assigned so that each PE in said portionof the plurality of PEs has its mutually exclusive matrix positionneighbors in at most two of the plurality of clusters of PEs, at leasttwo PEs in one cluster sharing a connection to their common neighbor inanother cluster when communicating to their mutually exclusive matrixposition neighbors through the cluster switch.
 2. An array processorcomprising: a plurality of processing elements(PEs), each PEcorresponding to a position of a matrix element where the position ofthe matrix element has at least a North, East, South, or West matrixposition neighbor, a pair of matrix neighbors is mutually exclusive whenone neighbor is either in the North or South direction relative to theposition of the matrix element and the other neighbor is either in theEast or West direction relative to the position of the matrix elementthe plurality of PEs arranged in a plurality of clusters, each clusterincluding a portion of the plurality of processing elements, the portionof PEs selected so that each PE in said portion of the plurality of PEshas its mutually exclusive matrix position neighbors in at most two ofthe plurality of clusters; and cluster switches connecting the pluralityof clusters, at least two PEs in each cluster sharing a connection totheir common neighbor to another cluster through the cluster switch. 3.The array processor of claim 2 wherein each cluster includes an equalnumber of processing elements.
 4. The array processor of claim 2 whereinat least one cluster includes a torus transpose pair of processingelements.
 5. The array processor of claim 2 wherein the cluster switchesprovide inter-PE connectivity equivalent to a torus connected array. 6.The array processor of claim 2 wherein the cluster switches providedirect communication between processing elements in a transposeprocessing element pair within a cluster.
 7. The array processor ofclaim 2 wherein the clusters of processing elements are scaleable. 8.The array processor of claim 2 wherein the processing elements of eachcluster are located in close physical proximity to each other.
 9. Thearray processor of claim 2 further comprising a single instructionmultiple data (SIMD) controller which broadcasts data to said pluralityof processing elements.
 10. The array processor of claim 9 wherein eachprocessing element performs a calculation and transmits the results ofthe calculation to a nearest neighbor processing element.
 11. The arrayprocessor of claim 2 wherein the clusters of processing elementscorrespond to slices of a torus array shifted and wrapped into acylinder.
 12. The array processor of claim 2 wherein each processingelement (PE) is defined as PE_(i,j), where i and j refer to therespective row and column PE positions within a conventionaltorus-connected array, and where i=0, 1, 2, . . . N−1 and j=0, 1, 2, . .. N−1, said PEs arranged in clusters PE_((i+a)(ModN), (j+N−a)(ModN)),for any i,j and for all a ε {0,1, . . . , N−1}.
 13. The array processorof claim 2 wherein each cluster switch multiplexes communications fromprocessing elements within a cluster for transmission to anothercluster.